Think of a NAS as a *nix (or Windows) machine without a monitor, keyboard and mouse connected. That's pretty much what most of them are. Of course, the models aimed at the consumer market usually don't have the latest and greatest CPU and such, but they can do pretty much anything you can do on any other type of server (depending on what OS and hardware your chosen NAS have).

I don't see why you wouldn't be able to. Personally, I'm using an Asustor AS-608T with 6x4TB HDD's in RAID 5 (formatted as NTFS). I have MySQL running 24/7, and have been doing so for about a year now without any issues, nor do I expect any that I wouldn't run into with any other server at some point or another. I access the NAS with a variety of devices, ranging from iPhones/iPads, Android phones and tablets, PC's running Linux, Windows and my MacBook. Heck, I even have my Nexus Player (Android TV) access the device. It doesn't matter to the devices what file system the NAS itself is running.

I don't see why you wouldn't be able to. Personally, I'm using an Asustor AS-608T with 6x4TB HDD's in RAID 5 (formatted as NTFS). I have MySQL running 24/7, and have been doing so for about a year now without any issues, nor do I expect any that I wouldn't run into with any other server at some point or another. I access the NAS with a variety of devices, ranging from iPhones/iPads, Android phones and tablets, PC's running Linux, Windows and my MacBook. Heck, I even have my Nexus Player (Android TV) access the device. It doesn't matter to the devices what file system the NAS itself is running.